POD-Galerkin reduced order methods for combined Navier-Stokes transport equations based on a hybrid FV-FE solver

TL;DR

This paper develops a novel POD-Galerkin reduced order modeling approach for hybrid FV-FE solvers applied to incompressible Navier-Stokes equations coupled with a transport equation, ensuring efficient simulation of complex fluid-transport phenomena.

Contribution

It introduces a new POD-Galerkin strategy that incorporates staggered meshes and a pressure reconstruction method for coupled Navier-Stokes and transport equations.

Findings

Validated against 3D manufactured test cases.

Analyzed a modified cavity benchmark with species transport.

Demonstrated accuracy and efficiency of the reduced order model.

Abstract

The purpose of this work is to introduce a novel POD-Galerkin strategy for the hybrid finite volume/finite element solver introduced in Berm\'udez et al. 2014 and Busto et al. 2018. The interest is into the incompressible Navier-Stokes equations coupled with an additional transport equation. The full order model employed in this article makes use of staggered meshes. This feature will be conveyed to the reduced order model leading to the definition of reduced basis spaces in both meshes. The reduced order model presented herein accounts for velocity, pressure, and a transport-related variable. The pressure term at both the full order and the reduced order level is reconstructed making use of a projection method. More precisely, a Poisson equation for pressure is considered within the reduced order model. Results are verified against three-dimensional manufactured test cases. Moreover a modified version of the classical cavity test benchmark including the transport of a species is analysed.